Question

An economist is studying the job market in Denver area neighborhoods. Let x represent the total...

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).

x 16 33 53 28 50 25
y 2 3 5 5 9 3

Given: Σx = 205    Σy = 27    Σx2 = 8063    Σy2 = 153    Σxy = 1061 r ≈ 0.758.

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x = ___
y = ____
= ____ + ___ x

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =
explained     %
unexplained     %

(f) For a neighborhood with x = 32 hundred jobs, how many are predicted to be entry level jobs? (Round your answer to two decimal places.)
______ hundred jobs

Homework Answers

Answer #1

c)

X̅=ΣX/n = 34.17
Y̅=ΣY/n = 4.50
ŷ = 0.031+0.131x

e)

coefficient of determination r2 = 0.575
explained = 57.5%
unexplained= 42.5%

f)

predicted value =0.031+0.131*32= 4.22
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